# A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 7 , 4 , and 1 , respectively. What is the rectangle's area?

Aug 15, 2017

The rectangle's area is $\sqrt{33}$ or $5.74$

#### Explanation:

Above is a drawing of the situation in question.

Since we have two sides of a right triangle, we can use the Pythagorean theorem to calculate the length of side B.

${a}^{2} + {b}^{2} = {c}^{2}$

Be sure to note that a and b here refer to the smaller sides of the triangle and the c refers to hypotenuse, which is different from the letters in our diagram!

${4}^{2} + {b}^{2} = {7}^{2}$

$16 + {b}^{2} = 49$

${b}^{2} = 33$

$b = \sqrt{33}$

Now, to calculate the area of the rectangle, we must multiple its length by its width. Side B is its length and we already know its width is 1, and since any number multiple by 1 is just itself, the area of the rectangle is $\sqrt{33}$, or $5.74$